1. Field of the Invention
The invention relates generally to flow measurement methods and systems. In particular, embodiments relate to flow measurements using Nuclear Magnetic Resonance (NMR) instruments.
2. Background Art
In industries where a flow of fluid is involved, measurements of flow parameters such as flow velocity and fluid viscosity are often required. Conventional flow measurement technologies include turbine flow meters and positive-displacement flow meters, both of which involve placement of moving parts in the flowing fluid. Moving pails, such as a turbine, disturb the flow pattern of the fluid, thus increasing the complexity of obtaining accurate measurements.
Non-invasive (low measurements such as ultrasonic meters and NMR sensors have certain advantages over conventional flow meters. These advantages include: excellent long-term repeatability, less sensitivity to fluid properties such as viscosity and pressure, higher accuracy, wider range of linearity, and lower cost of maintenance due to the lack of moving parts. Thus, non-invasive flow measurements are particularly well-suited for downhole tools in the oil and gas industry.
U.S. Pat. No. 6,046,587 issued to King et al. discloses methods and apparatus for measuring flow velocity of multiphase fluids flowing in a pipeline. The King et al. patent teaches using the ratio of FID amplitudes of signals acquired with different delay times to infer flow velocity using a single NMR sensor. However, the FID signal is difficult to measure using permanent magnets because static magnetic field variations will result in signals that decay too fast for reliable detection. Moreover, the King et al. methods for determining flow velocity do not account for the fact that there is a distribution of (low velocity in a pipe. In another embodiment, the King et al. apparatus consists of two separated NMR sensors. The flow-velocity and fluid volumes for multiphase fluid flow are computed from FID measurements from the two sensors. However, the computation requires prior knowledge of the fluid T1 distributions.
As known in the field of NMR imaging, to obtain 3-D proton density information in density imaging, a magnetic field gradient needs to be used across a sample to be measured, resulting in a variation of frequency ωa over the sample. The magnetic field gradient can also be used to measure flow properties. The magnetic field gradient causes a periodicity in spin density in the sample. In practice, by sending a sequence of RF pulses into the sample, an echo signal can be generated. A typical sequence used in various applications is referred to as a spin-echo sequence, including a 90° pulse, which rotates the net magnetization from the X direction down to the Y-Z plane, followed by a 180° pulse, which rotates the magnetization by 180° about the Y axis. The 180° pulse re-phases the magnetization thus producing a signal, i.e., the spin-echo signal. Intuitively, an RF pulse can cause spin excitations in a fluid, and if the fluid is flowing, a group of nuclei in excited state is carried by the flow. An echo signal in a time axis carries information on the flow properties such as the flow velocity.
In addition to flow properties, other reservoir fluid properties can be measured using an NMR module in a downhole tool, such as the fluid sampling tool disclosed in U.S. Pat. No. 6,346,813 B1 issued to Kleinberg. An example of formation fluid tester tool is the Modular Formation Dynamics Testing tool marketed under the trade name of MDT™ by Schlumberger Technology Corp. (Houston, Tex.).
FIG. 1 shows an exemplary formation fluid testing tool body 10 (e.g., an MDT™ tool) that houses the following modules: an electric power module 11; a hydraulic power module 12; a probe module 13, which may be deployed to make a hydraulic seal with the formation; an optical fluid analyzer module 14; an NMR module 15, a multi-sample module 16, and a pumpout module 17. In addition, the tool body 10 may enclose a processor and a memory for downhole data collection and processing. The tool body 10 is designed to work in harsh downhole environments.
The NMR module 15 may include an NMR sensor, which includes a magnet that can produce a substantially homogeneous static magnetic field over the volume of the fluid sample. In addition, the NMR sensor includes at least one coil that can produce pulsed field gradients (PFG) of defined amplitudes and time durations across the sample volume. A homogeneous static magnetic field in combination with a PFG can provide measurements with better signal-to-noise ratios because a larger sample volume is resonated, as compared to a static magnetic field having a static field gradient, which can only excite a small portion of the sample (a “sample slice”) to resonate. The NMR sensor also includes a coil (an RF antenna) for producing RF pulses. The magnetic moment of the RF antenna is substantially perpendicular to the magnetic moment of the static magnetic field.
U.S. Pat. No. 6,952,096, issued to Freedman on Oct. 4, 2005, and also assigned to the assignee of the present invention, discloses an NMR sensor and a pulse sequence used to measure a flow velocity. The NMR sensor includes some basic elements such as a magnet to generate a substantially homogeneous “base” field and RF antenna to excite a portion of the flow.
FIG. 2A shows an illustration of an NMR sensor 20 disclosed by Freedman in U.S. Pat. No. 6,952,096, for determining flow velocity and other properties of a fluid flowing in a flowline (or flow pipe) 22. A magnet 24 and an RF antenna 26 are included in the NMR sensor 20.
The flowline 22 includes a pre-polarization section 28 that is upstream of an investigation section 29. The magnet 24 is disposed around both the pre-polarization section 28 and the investigation section 29. The magnet 24 may be a permanent magnet or an electromagnet. The flowline 22 is typically made of a non-conductive and non-magnetic material, such as a composite or polymer material. However, if the flowline 22 is made of a conductive or magnetic material (e.g., steel), then the antenna 26 should be located inside the flowline.
For the NMR sensor 20 shown in FIG. 2A, the antenna (solenoid coil) 26 functions as both a transmitter and a receiver. When functioning as a transmitter, the RF antenna emits RF electromagnetic pulses along the direction of the RF antenna. The RF antenna 26 substantially covers the investigation section 29 of the flowline 22.
The NMR measurements include a suite of variable wait time (W) measurements. Prior to each wait time (W), the magnetization is first spoiled by pulses designed to “kill” the magnetization so that MX=MY=MZ=0. Following the spoiling pulse and the wait time, a 90° pulse followed by a 180° pulse (e.g. a spin-echo pulse) is applied to the transmitter to generate a spin echo. The measurements are repeated for a number of different wait times. Multiple 180° pulses may be applied to produce multiple spin-echo signals.
The amplitudes of the detected spin-echo signals for the different wait times depend on flow velocity, wait time, receiver and transmitter antenna lengths, magnet pre-polarization length, and the T1 distribution of the fluid. All of these parameters, except the flow velocity and the T1 distribution of the fluid, are either fixed by the sensor design or by the pulse sequence. If sufficient sets of measurements are available, these parameters may be derived by fitting the measured signals to a proper model that simulates the NMR response of the flowing fluid. That is, the data may be interpreted by forward modeling.
A theoretical forward model can be used to simulate the echo signals for any combination of the aforementioned pulse sequence, sensor parameters, flow velocity, and T1 distribution. The forward model may be used iteratively in an inversion to determine the apparent flow velocity and T1 distribution. Alternatively, if the flow velocity is known from other measurements, the forward model can be lit by inversion to determine the T1 distribution.
FIG. 2B shows that the velocity- and position-dependent polarization profile f(v,z) over the length la of the receiver coil (shown as 26 in FIG. 2A) is made of two parts. The first part comes from fresh spins that are “pre-polarized” as they travel in the static magnetic field into the receiver during the wait time W. The second part comes from spins that were in the receiver coil and are “re-polarized” during the wait time. The pre-polarization length lp shown in FIGS. 2A and 2B corresponds to the length of the pre-polarization region 28.
The polarization function is given by
                                          f            ⁡                          (                              v                ,                z                            )                                =                      1            -                          exp              (                              -                                                      T                    ⁡                                          (                                              z                        ,                        v                                            )                                                                            T                    1                                                              )                                      ,                            (        1        )            where T(z, v) is the polarization time for a spin with position z and velocity v, and T1 is the longitudinal relaxation time of the spins. The polarization time, T(z,v), is defined as:
                                          T            ⁡                          (                              z                ,                v                            )                                =                                                                                          l                    p                                    +                  z                                v                            ⁢                                                          ⁢              for              ⁢                                                          ⁢              0                        ≤            z            ≤                          v              ·              W                                      ⁢                                  ⁢                  and          ,                                    (                  2          ⁢          a                )                                          T          ⁡                      (                          z              ,              v                        )                          =                              W            ⁢                                                  ⁢            for            ⁢                                                  ⁢                          v              ·              W                                <          z          ≤                                    l              a                        .                                              (                  2          ⁢          b                )            
It is clear from the above equations that the polarization function, ƒ(v,z), also depends on lp, W, and T1. Those dependencies are implicit in Eq. 1. The polarization time, T(z, v), is used to simplify the notation, but depends on lp and W as z ranges over the defined intervals. These equations can be more easily understood following a discussion of the variable wait time (VWT) pulse sequence shown in FIGS. 3A and 3B.
FIG. 3A shows a suite of VWT pulses consisting of N measurements. N is typically on the order of 10. At the conclusion of each measurement in the suite, one or more spoiling pulses (collectively denoted by the pulse S) are applied to destroy any remnant magnetization before starting the wait lime for the next measurement. The duration and frequencies of the spoiling pulses are instrument dependent and can be determined empirically.
As shown schematically by the kth measurement in FIG. 3B, following each wait time a 90° excitation pulse is applied to rotate the longitudinal magnetization into the transverse plane. The signal from the transverse magnetization rapidly de-phases due to inhomogeneity (or other factors) in the static magnetic field, but is refocused by the 180° pulse to produce a spin-echo signal. After the spin-echo signal is acquired a spoiling pulse is applied to remove the magnetization of the spins within the receiver coil. Other VWT sequences similar to the one shown in FIGS. 3A and 3B can also be used to observe FID signals instead of a spin-echo signal. Both the inversion-recovery and the saturation-recovery pulse sequences are generally referred to as “T1-relaxation investigation pulse sequences.”
The pulse sequence used to acquire the NMR signals (FID or spin-echo signals) are generally referred to as an “acquisition pulse sequence.” An acquisition pulse sequence may include a single 90° pulse, a spin-echo pulse (i.e., a 90° pulse followed by a 180° pulse), and the variants of the spin-echo pulse such as the Carr-Purcell-Meiboom-Gill (CPMG) sequence, i.e., multiple 180°, refocusing pulses following a single 90° excitation pulse.
The “variable wait time pulse sequence” as shown in FIGS. 3A and 3B comprises a spoiling pulse, a wait time, and an acquisition pulse sequence. The spin-echo pulse sequence and its variants (e.g., CPMG) are generally referred to as a “spin-echo pulse sequence.” That is, a “spin-echo pulse sequence” not only includes a single 90° pulse and a single 180° pulse, but also may include multiple 180° pulses after the 90° pulse.
During each wail time, fresh or pre-polarized spins move into the antenna region. Equation (2a) shows that in the region. 0≦z≦vW, fresh spins have entered the antenna during the wait time. The length of this region depends on v and W. The polarization time for these fresh spins is independent of W. Instead, it depends on the duration that the spins have been exposed to the static magnetic field since they entered the field of the permanent magnet. This is because this portion of the fluid is outside the transmitter/receiver antenna (shown as 26 in FIG. 2A) when the spoiling pulse is applied and the magnetizations of the spins in this portion of the fluid are not “killed” by the spoiling pulse. On the other hand, as can be seen from Eq. (2b), the re-polarization of the spins in the adjoining region of length, i.e. , from v·W to la, is controlled by W because these spins were in the transmitter/receiver region when the spoiling pulse was applied. The magnetizations of these spins were removed by the spoiling pulse, and any polarization detected by the receiver is due to re-polarization during W. If W is long or v is fast enough such that v·W exceeds the antenna length, then only fresh spins (those that enter the receiver antenna after the spoiling pulse) are measured and the polarization function is independent of W.
U.S. Pat. No. 6,841,996, issued to Madio et al. on Jan. 11, 2005, discloses methods for measuring the velocity of fluids flowing through a flowline of a fluid sampling tool. The method exploits the fact that there is a spin echo signal phase shift between different wait time measurements in a VWT pulse sequence. The measured phase shifts are proportional to both the flow velocity and a static magnetic field gradient. In addition, Madio et al. show a linear relationship between the phase difference of odd and even echoes and the product of the flow velocity and the static magnetic field gradient, up to a flow velocity of 6 cm/sec. At higher flow velocities, the phase difference is no longer an adequate velocity indicator.
Forward models can be used to predict the NMR sensor signals, which depends on the flow velocity, the distribution of T1, the wait time, and geometrical parameters such as the antenna length, the magnet pre-polarization length, and the radius of the flowline. For a given wait lime and a sensor design, the only variables in the forward model are the flow velocity and the T1 distribution of the fluid. The flow velocity and T1distribution are determined by inversion. The forward model is derived in the following paragraphs.
To accurately model die NMR signals from flowing fluids, the fact that the velocity profile of a laminar flow for a viscous fluid flowing in a pipe is parabolic should be taken into account. See, e.g., Streeter, “Fluid Mechanics.” McGraw-Hill Book Co., 5th Edition. p. 244. In a laminar flow, the maximum flow velocity, vm, occurs at the axis of the pipe, while the velocity is zero at the wall of the pipe. The laminar flow regime in circular pipes is characterized by the values of Reynolds number, R≦2000˜3000, where the exact upper limit for laminar flow depends on the surface roughness of the pipe. The Reynolds number is defined by
                              R          =                                    2              ⁢                              r                o                            ⁢              v              ⁢                                                          ⁢              ρ                        η                          ,                            (        3        )            where ro is the radius of the flowline, v is the average flow velocity, ρ is the fluid mass density, and η is the viscosity of the fluid. In contrast to a laminar flow, turbulent flow has a chaotic component and is much more difficult to model. One feature of turbulent flow is a flattening of the velocity parabolic profile. FIG. 4 shows the velocity profiles for laminar flow and non-laminar flow in a circular pipe.
For a laminar flow the velocity profile is parabolic and can be written in the form,
                              v          ⁡                      (            r            )                          =                              -                                          (                                                      r                    2                                    -                                      r                    0                    2                                                  )                                            r                0                2                                              ⁢                                          ⁢                      v            m                                              (                  4          ⁢          a                )            where vm is the maximum flow velocity on the axis of the flowline (i.e., at r=0) as shown in FIG. 4. It follows from Eq. (4a) that the average flow velocity with a laminar flow is vm/2. While Eq. (4a) describes a commonly used model for laminar flow, an alternative laminar flow model may be described as follows;
                              v          ⁡                      (            r            )                          =                                            v              m                        ⁡                          (                              1                -                                  r                                      r                    0                                                              )                                            1            /            n                                              (                  4          ⁢          b                )            where n is typically between 5 and 10.
The velocity profile for the non-laminar flow depicted in FIG. 4 can be described by the following equations:
                                          v            ⁡                          (              r              )                                =                                                    v                m                            ⁢                                                          ⁢              for              ⁢                                                          ⁢              0                        ≤            r            ≤            a                          ,                                  ⁢        and        ,                            (                  5          ⁢          a                )                                          v          ⁡                      (            r            )                          =                                            -                                                                    {                                                                                            (                                                      r                            -                            a                                                    )                                                2                                            -                                                                        (                                                                                    r                              0                                                        -                            a                                                    )                                                2                                                              }                                    ⁢                                                                          ⁢                                      v                    m                                                                                        (                                                                  r                        0                                            -                      a                                        )                                    2                                                      ⁢                                                  ⁢            for            ⁢                                                  ⁢            a                    ≤          r          ≤                                    r              0                        .                                              (                  5          ⁢          b                )            
The flow models described above can be used to derive flow profiles in
conjunction with NMR signals.
FIG. 5 illustrates a spin-echo pulse sequence that can be used to measure a flow velocity, as disclosed by Carr and Purcell (the Physical Review, v. 94, no. 3, pp. 630-638, 1954). The ratio of even to odd spin echo amplitude, e.g., the ratio between the amplitudes of the even spin-echo signal 52 and the odd spin-echo signal 51′ is proportional to the flow velocity. Thus, by measuring the amplitudes of the spin-echo signals, the flow velocity can be derived.
U.S. Pat. Nos. 6,518,757, 6,518,758, 6,528,995, 6,531,869, 6,538,438, 6,710,596, 6,642,715, issued to Speier et al., and also assigned to the assignee of the present invention, disclose obtaining flow velocity information in the formation from the amplitude of the spin echo.
U.S. Pat. No. 6,856,132 issued to Appel et al., discloses obtaining flow velocity information in the formation in the presence of a static magnetic field gradient.